%CERTIFY%

Jets with pileup in 2011

In-time pile-up

The result of additional interactions in the current bunch crossing. The amount of in-time pile-up is described (on average) by the number of reconstructed primary vertices in an event, N_PV. However, other variables may provide a more ideal parametrization of in-time pile-up. For example, the number of tracks not associated with the hard scatter primary vertex, N_trk^out, may be a more precise measure of pile-up activity, and it is less sensitive to vertex reconstruction efficiencies.

Out-of-time pile-up

Because the integration times in the calorimeter span many successive bunch crossings, minimum bias interactions from several preceding and some following bunch crossings may affect the response of the calorimeter to in-time signals. The effect of out-of-time pile-up depends on several factors that are specific to each event. Signal shaping in the calorimeter is designed such that out-of-time pileup should have an overall negative effect that cancels the positive effect from in-time pile-up on average. However, this only works if the bunch intensity is constant over the integration time of the calorimeter. For example, at the beginning of a bunch train there is insufficient out-of-time pile-up to cancel the in-time pile-up, so the calorimeter response is systematically higher for these events.

Currently, we do not have a way to directly measure the number of interactions in preceding and following bunch crossings, so we use the instantaneous luminosity to roughly estimate the amount of out-of-time pile-up. The variable μ is the mean number of inelastic interactions per bunch crossing, calculated directly from the instantaneous luminosity, inelastic cross-section, and beam parameters for the luminosity block that contains the event of interest. Work is ongoing to provide a more precise estimate of the out-of-time pile-up, for example using the BCID-specific luminosity to take into account variations in bunch intensity.

Effect on the jet energy scale

Perhaps the largest effect that pile-up has on reconstructed jets is to shift the jet energy scale. We are primarily interested in measuring and correcting for this shift, though studies of other pile-up effects on jets are also ongoing.

Pile-up interactions result in both diffuse, low-p_T and point-like, high-p_T energy deposits in the calorimeter. The average shift in the JES is due to the low-p_T component of pile-up. Diffuse in-time pile-up contributes a fixed amount of energy (dependent on jet η) to each jet for every additional minimum bias interaction. On the other hand, out-of-time pileup can either add or subtract energy from the jet, depending on the distribution in time of contributions from surrounding bunch crossings.

The effect of diffuse in-time and out-of-time pile-up is to induce an additive offset in the jet energy scale, and we expect this offset to depend linearly on the numbers of additional in-time and out-of-time interactions. Thus, we propose the following form for an offset correction:

Both A and B must depend on jet η, and they must be determined separately for each type of jet (algorithm, radius, EM vs. LC). The quantities μ^ref and N_PV^ref are used to control the output energy scale of the correction, which should match the assumed input energy scale of any subsequent jet calibration.

To begin, we have determined a jet p_T offset of this form by matching reconstructed jets to truth jets in simulated QCD dijet events; the next section is a description of the resulting correction.

MC-based offset correction

The correction uses two variables to parametrize pile-up: the number of primary interactions in an event (N_PV) and the number of average interactions in a lumi block (μ). The correction is p_T independent, and it is given in seven |η| bins: 0.0-0.3, 0.3-0.8, 0.8-1.2, 1.2-2.1, 2.1-2.9, 2.9-3.5, 3.5-5.0. In addition, the correction depends on two extra parameters that connect the correction with the JES: the reference values of N_PV and μ. These should be taken from the MC sample from which the JES was derived, and should be equal to the mean values of N_PV and μ in that sample. The correction should be applied before the JES, taking into account the reference values of N_PV and μ.

Correction for Release 16 (MC10b)

The latest version of this correction was presented at the 2011 ATLAS hadronic calibration workshop at SLAC(https://indico.cern.ch/getFile.py/access?contribId=29&sessionId=0&resId=0&materialId=slides&confId=132005), and all the plots supporting it can be found here:

• AntiKt6 EM jets http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt6Topo_correctionpT.html
• AntiKt6 LC jets http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt6LCTopo_correctionpT.html
• AntiKt4 EM jets http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt4Topo_correctionpT.html
• AntiKt4 LC jets http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt4LCTopo_correctionpT.html

Correction for Release 17 (MC11a)

• AntiKt6 EM jets http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt6Topo_correctionMC11.html
• AntiKt6 LC jets http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt6LCTopo_correctionMC11.html
• AntiKt4 EM jets http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt4Topo_correctionMC11.html
• AntiKt4 LC jets http://csandova.web.cern.ch/csandova/trackjets/D3PD/AntiKt4LCTopo_correctionMC11.html

Code

Show MC-based offset correction code Hide MC-based offset correction code

///=========================================                                                                                                                                       
/// GetOffsetCorrection NPV                                                                                                                                                        
///=========================================                                                                                                                                       
double AnalysisBase::GetOffsetNPV(Double_t jetEta, Double_t mu, Int_t NPV, TString tag, Int_t NPVref, Int_t MUref, bool m_fDebug) {


  // Offset correction table                                                                                                                                                       

  //slope and intercept                                                                                                                                                            
    const static Double_t slope_MC10b_AKt6_topoEM[7] = {
    0.554206,0.560879,0.615631,0.604061,0.643603,0.627901,0.645477};
  const static Double_t intercept_MC10b_AKt6_topoEM[7] = {
    0.113253,0.0988858,0.0229146,0.0216436,-0.117142,-0.251135,-0.330684};
    const static Double_t slope_MC10b_AKt6_lct[7] = {
    0.841648,0.856677,0.919961,0.92832,0.909487,0.913625,0.754934};
  const static Double_t intercept_MC10b_AKt6_lct[7] = {
    0.157548,0.130792,0.0549006,0.0753573,-0.131852,-0.373156,-0.412353};

    const static Double_t slope_MC10b_AKt4_topoEM[7] = {
    0.297376,0.2657,0.287447,0.316899,0.340274,0.362528,0.363839};
  const static Double_t intercept_MC10b_AKt4_topoEM[7] = {
    0.0262287,0.0143564,-0.0311566,-0.0125061,-0.124887,-0.185109,-0.238533};
    const static Double_t slope_MC10b_AKt4_lct[7] = {
    0.406266,0.375533,0.4012,0.449796,0.451956,0.508713,0.400553};
  const static Double_t intercept_MC10b_AKt4_lct[7] = {
    0.0241725,0.0339716,-0.0238977,-0.0173475,-0.16973,-0.300495,-0.30317};

  const static Double_t slope_MC11_AKt6_topoEM[7] = {
    0.55317,0.566214,0.592801,0.595636,0.642784,0.570846,0.611743};
  const static Double_t intercept_MC11_AKt6_topoEM[7] = {
    0.077248,0.0651614,0.05082,0.0694886,-0.104221,-0.368601,-0.365378};
  const static Double_t slope_MC11_AKt6_lct[7] = {
    0.87382,0.937068,0.931847,1.04197,1.04428,0.880914,0.756087};
  const static Double_t intercept_MC11_AKt6_lct[7] = {
    0.0583321,0.148085,0.191317,0.157699,-0.129749,-0.528437,-0.412108};


  const static Double_t slope_MC11_AKt4_topoEM[7] = {
    0.252522,0.285027,0.303536,0.305193,0.356775,0.338547,0.362128};
  const static Double_t intercept_MC11_AKt4_topoEM[7] = {
    0.153442,-0.0160134,-0.0193743,-0.0919976,-0.168367,-0.250434,-0.211702};
  const static Double_t slope_MC11_AKt4_lct[7] = {
    0.387692,0.439022,0.453936,0.476658,0.512217,0.500963,0.404941};
  const static Double_t intercept_MC11_AKt4_lct[7] = {
    0.191242,-0.0123295,-0.0152481,-0.0551463,-0.23288,-0.394158,-0.255641};


  if (m_fDebug) cout << "In GetOffsetNPV()" << endl;

  double jet_NPV_offset = 0.0;


  int eta_index = -1;

  if(fabs(jetEta) <= 0.3)                       eta_index = 0;
  if(fabs(jetEta) > 0.3 && fabs(jetEta) <= 0.8) eta_index = 1;
  if(fabs(jetEta) > 0.8 && fabs(jetEta) <= 1.2) eta_index = 2;
  if(fabs(jetEta) > 1.2 && fabs(jetEta) <= 2.1) eta_index = 3;
  if(fabs(jetEta) > 2.1 && fabs(jetEta) <= 2.9) eta_index = 4;
  if(fabs(jetEta) > 2.9 && fabs(jetEta) <= 3.5) eta_index = 5;
  if(fabs(jetEta) > 3.5 && fabs(jetEta) <= 5.0) eta_index = 6;



  if(tag.Contains("AKt6_TopoEM_MC10b")) {
    jet_NPV_offset = slope_MC10b_AKt6_topoEM[eta_index] * (NPV-NPVref) + intercept_MC10b_AKt6_topoEM[eta_index] * (mu-MUref) ;
  }
  else if(tag.Contains("AKt6_LCTopo_MC10b")) {
    jet_NPV_offset = slope_MC10b_AKt6_lct[eta_index] * (NPV-NPVref) + intercept_MC10b_AKt6_lct[eta_index] * (mu-MUref);
  }
  else if(tag.Contains("AKt4_TopoEM_MC10b")) {
    jet_NPV_offset = slope_MC10b_AKt4_topoEM[eta_index] * (NPV-NPVref) + intercept_MC10b_AKt4_topoEM[eta_index] * (mu-MUref) ;
  }
  else if(tag.Contains("AKt4_LCTopo_MC10b")) {
    jet_NPV_offset = slope_MC10b_AKt4_lct[eta_index] * (NPV-NPVref) + intercept_MC10b_AKt4_lct[eta_index] * (mu-MUref);
  }
  else if(tag.Contains("AKt6_TopoEM_MC11")) {
   jet_NPV_offset = slope_MC11_AKt6_topoEM[eta_index] * (NPV-NPVref) + intercept_MC11_AKt6_topoEM[eta_index] * (mu-MUref) ;
  }
  else if(tag.Contains("AKt6_LCTopo_MC11")) {
    jet_NPV_offset = slope_MC11_AKt6_lct[eta_index] * (NPV-NPVref) + intercept_MC11_AKt6_lct[eta_index] * (mu-MUref);
  }
  else if(tag.Contains("AKt4_TopoEM_MC11")) {
    jet_NPV_offset = slope_MC11_AKt4_topoEM[eta_index] * (NPV-NPVref) + intercept_MC11_AKt4_topoEM[eta_index] * (mu-MUref) ;
  }
  else if(tag.Contains("AKt4_LCTopo_MC11")) {
    jet_NPV_offset = slope_MC11_AKt4_lct[eta_index] * (NPV-NPVref) + intercept_MC11_AKt4_lct[eta_index] * (mu-MUref);
  }


  else cout << "WARNING: cannot find offset correction for tag = " << tag << "; Please use a supported tag." << endl;


  // Some debugging                                                                                                                                                                
  if (m_fDebug)     cout << "Eta = " << jetEta
                         << " ; eta bin in graph = " << eta_index
                         << " ; mu = " << mu
                         << " ; NPV = " << NPV
                         << " ; Jet NPV offset = " <<  jet_NPV_offset
                         << " ; Tag = " <<  tag
                         << endl;


  // Done                                                                                                                                                                          
  return jet_NPV_offset;

}

Instructions

The correction returns a number that should be subtracted from the p_T of the jet (uncalibrated, i.e. no JES) in GeV. It has 6 input parameters: N_PV, μ, jet η, N_PV^ref, μ^ref, and a tag. The tag tells the correction which jet collection you are interested in. This is the list of tags that should be used:

• "AKt6_TopoEM_MC10b"
• "AKt6_LCTopo_MC10b"
• "AKt4_TopoEM_MC10b"
• "AKt4_LCTopo_MC10b"
• "AKt6_TopoEM_MC11"
• "AKt6_LCTopo_MC11"
• "AKt4_TopoEM_MC11"
• "AKt4_LCTopo_MC11"

The correction should be applied as follows:

where Offset is obtained from the GetOffsetNPV() function defined in the code above, parametrized by the variables explained here and the tags in the list (a different implementation can be found in JetCalibTools to use within ATHENA). If for example you want to use the JES from MC10b, you should use NPVref=6, MUref=8 and the tags with "MC10b". To obtain the correction for an AntiKt6 LC jet, you would call GetOffsetNPV(jetEta, mu, NPV, "AKt6_LCTopo_MC10b", 6, 8, false).

In-situ validation techniques

Track-jet validation

γ-jet p_T balance

Systematic uncertainties

Show old tower studies Hide old tower studies

Show Pileup in MC10b - old Hide Pileup in MC10b - old

Show Pileup in Data - old Hide Pileup in Data - old

Pileup in Data

Effect of bunch spacing on raw calorimeter energy density

Comparison between 2010 PeriodI , 2011 run178109 (75ns bs) and run 179153 (50ns bs)

As an initial study, we looked at the differences between the average calorimeter tower energy vs. the number of primary vertices for late 2010 data, early 2011 75ns data and recent 2011 50ns data. While these plots show that there are significant differences between the data periods, it does not illustrate why. It was not clear if the bunch spacing alone was the cause of the differences. The next set of plots shows the differences between several 50ns runs, indicating that the bunch spacing alone is not the cause of the varying average tower energy.

Error: (3) can't find h_tower_E_NV_Eta_0_08.150ns.75ns.50ns.comp.png in Sandbox

Error: (3) can't find h_tower_E_NV_Eta_32_5.150ns.75ns.50ns.comp.png in Sandbox

Comparison between several runs with 50ns bunch spacings

As mentioned above, bunch spacing alone does not explain why there is a run-by-run difference in the average calorimeter tower energy, as shown below.

Error: (3) can't find h_tower_E_NV_Eta_0_50ns_runcomp.png in Sandbox	Error: (3) can't find h_tower_E_NV_Eta_1_50ns_runcomp.png in Sandbox	Error: (3) can't find h_tower_E_NV_Eta_2_50ns_runcomp.png in Sandbox	Error: (3) can't find h_tower_E_NV_Eta_3_50ns_runcomp.png in Sandbox
Error: (3) can't find h_tower_E_NV_Eta_4_50ns_runcomp.png in Sandbox	Error: (3) can't find h_tower_E_NV_Eta_5_50ns_runcomp.png in Sandbox	Error: (3) can't find h_tower_E_NV_Eta_6_50ns_runcomp.png in Sandbox	Error: (3) can't find h_tower_E_NV_Eta_7_50ns_runcomp.png in Sandbox

Run-by-run luminosity, bunch, and tower based pileup offset information

In order to determine the dependence of the average calorimeter energy, and thus the tower based offset correction, we list all of the quantities of interest in the table below. The plots these numbers are derived from are in the Notes section below.

Data Period	Run Number	Luminosity			<mu>	RMS(mu)	Bunch Spacing	Average Bunch Train Length	Slope of tower based <Jet ET Offset> vs. NPV (GeV / Vertex) AntiKt4,AntiKt6
		Recorded [1/pb]	L1_J15 [1/nb]	EF_zerobias_NoAlg [1/nb]					0< |eta| < 0.3	3< |eta| < 0.8	0.8< |eta| < 1.2	1.2< |eta| < 2.1	2.1< |eta| < 2.8	2.8< |eta| < 3.2	3.2< |eta| < 4.5
B2	178044	4.7	3.5	3.1			75ns	1727ns	0.35, 0.65	0.37, 0.69	0.39, 0.77	0.37, 0.75	0.42, 0.89	0.54, 1.2	0.35, 0.80
B2	178109	6.5	4.8	4.3			75ns	1727ns
D1	179710	4.3	4.4	2.1	5.9	1.4	50ns	1651ns	0.50, 0.92	0.51, 0.95	0.53, 1.0	0.49, 0.99	0.58, 1.2	0.71, 1.6	0.36, 0.86
D2	179804	7.4	5.4	3.7	6.4	1.5	50ns	1701ns	0.51, 0.94	0.52, 0.97	0.54, 1.1	0.51, 1.0	0.58, 1.2	0.73, 1.6	0.38, 0.86
D3	180124	7.6	5.3	3.8	5.1	1.2	50ns	1704ns	0.44, 0.79	0.46, 0.84	0.46, 0.91	0.44, 0.87	0.52, 1.1	0.64, 1.4	0.35, 0.86
D3	180139	7.7	3.4	3.8	6.1	1.1	50ns	1704ns	0.47, 0.84	0.47, 0.86	0.48, 0.93	0.45, 0.89	0.53, 1.1	0.65, 1.4	0.38, 0.88
D4	180153	8.8	6.0	4.4	5.4	1.2	50ns	1704ns	0.44, 0.79	0.46, 0.85	0.48, 0.91	0.46, 0.89	0.53, 1.1	0.65, 1.4	0.40, 0.87
D4	180164	19.1	9.8	9.6	5.8	1.3	50ns	1704ns	0.50, 0.91	0.51, 0.94	0.54, 1.0	0.49, 0.98	0.58, 1.2	0.72, 1.5	0.40, 0.88
D5	180225	17.1	10.2	8.5	5.3	1.1	50ns	2833ns	0.36, 0.67	0.38, 0.70	0.39, 0.75	0.39, 0.76	0.45, 0.93	0.57, 1.2	0.38, 0.84
D6	180309	9.5	2.9	4.8	6.7	0.9	50ns	2833ns	0.38, 0.71	0.41, 0.74	0.40, 0.80	0.40, 0.79	0.47, 0.97	0.58, 1.3	0.40, 0.87
D6	180400	14.5	2.8	3.5	6.2	1.0	50ns	3318ns
D7	180481	21.1	4.2	5.4	6.0	1.1	50ns	3318ns	0.38, 0.68	0.38, 0.70	0.39, 0.75	0.39, 0.76	0.45, 0.92	0.57, 1.2	0.35, 0.83
E1	180636	24.1	5.1	6.6	5.8	1.1	50ns	3318ns	0.35, 0.64	3.36, 0.66	0.37, 0.72	0.37, 0.71	0.43, 0.87	0.54, 1.1	0.36, 0.77
E1	180710	12.1	1.8	6.8	7.1	0.9	50ns	3084ns	0.34, 0.60	0.33, 0.63	0.35, 0.68	0.35, 0.69	0.40, 0.81	0.51, 1.1	0.35, 0.78

Notes:

• Trash.AtlasRunQuery result for these runs (cached), including trigger information, luminosity and LHC info.
• The "Average Bunch Train Length" is a weighted average, accounting for the probability that a given event is in a given bunch train. (We assume that all bunches are equally intense, which is not a very good approximation.)
  • Thus, the probability of an event occurring within the first 400ns of a bunch train is just the ratio of 400ns to this average length.
• The luminosities are calculated using iLumiCalc:
  • iLumiCalc results page for L1_J15.
  • iLumiCalc results page for EF_zerobias_NoAlg.
  • GRL for only these runs.
    • This is a derivative of the data11_7TeV.periodAllYear_DetStatus-v13-pro08-02_JetEtMiss.xml GRL obtained from the GRL generator page here).

Error: (3) can't find OffsetAnalysis_mu_L1J15_ZB_overlay.png in Sandbox

• While the run-by-run information is shown above, the average offset vs. NPV slopes will be used for the pileup uncertainty estimate for the summer conference. For reference, below are the average (over all 50ns runs) constituent multiplicity for AntiKt4 and AntiKt6 TopoTower jets:

Error: (3) can't find nConst_vs_eta_akt4_ZeroBias.png in Sandbox

Error: (3) can't find nConst_vs_eta_akt6_ZeroBias.png in Sandbox

• With the average constituent multiplicities above and the average tower level E_T offset (below left), the average jet E_T offsets are shown below.

Error: (3) can't find offset_tower_energy_et.png in Sandbox

Error: (3) can't find offset_jet_energy_et_akt4.png in Sandbox

Error: (3) can't find offset_jet_energy_et_akt6.png in Sandbox

These plots can then be combined in a more useful form, the average jet transverse energy offset as a function of NPV for 7 eta bins, as shown below. These plots represent all of the 50ns data above modulo run 180400.

Error: (3) can't find h_data_jet_energy_offset_vs_NV_fit_akt4_formatted.png in Sandbox

Error: (3) can't find h_data_jet_energy_offset_vs_NV_fit_akt6_formatted.png in Sandbox

2011 Jet Pileup uncertainty from the RMS bias between data and MC10a

While we are not in a position to provide a pileup offset correction, it is possible to characterize the uncertainty on the JES calibration due to pileup in the 2011 data. To do this, we compare the difference between the average change in jet transverse energy pileup offset per additional vertex (Average Jet ET offset/NPV) between 50ns 2011 data and currently, MC10a minbias events. This comparison is shown in the below plot, which is derived from the previous two plots as well as the analogous ones for MC10a. Error: (3) can't find h_slope_eta_formatted_final.png in Sandbox

With this information as well as the average number of vertices in the 50ns data and the width of this distribution, shown below, we can define a positive and negative RMS bias, defined as:

Below are the calculated RMS biases between the 50ns data and MC10a for AntiKt4 and AntiKt6 Tower jets at EM scale for a , chosen because for this number of vertices, the average calorimeter tower energy is closest to zero, and . Using the difference between the negative and positive bias with the current EM+JES calibration, a relative jet pileup uncertainty can be calculated for jets of various in the defined regions.

Error: (3) can't find NVertices_fit.png in Sandbox

Error: (3) can't find h_RMS_akt4_slope_eta_formatted.png in Sandbox

Error: (3) can't find h_RMS_akt6_slope_eta_formatted.png in Sandbox

%RESPONSIBLE% JohnBackusMayes
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